ME 452: Machine Design II Project 1 - Fall 2009 Deliverable Due: Monday, September 14, 2009 Final Report Due: Friday, October 2, 2009 (Before 4:30 pm in the design offices, room 300 ME) This project is to be completed by each student individually. Backgro
ME 360 Control Systems
Cramers Rule for Solving A System of Linear Algebraic Equations
Given a set of linear algebraic equations
[A]cfw_x = cfw_b,
we can solve the equations for the vector cfw_x using Cramers Rule. An illustration
of how to apply Cramers
Bode Diagrams (Plots)
A better (unique) way to graphically display the frequency response!
Bode Magnitude Plot:
plots the magnitude of G(j) in decibels w.r.t. logarithmic frequency, i.e.,
G ( j )
dB
= 20log10 G ( j )
vs
log10
Bode Phase Plot:
plots the ph
ME 3600
OUT: 01/22/2016
HOMEWORK SET 2 SOLUTIONS
Spring 2016
DUE: 01/29/2016
Use a separate sheet to answer each problem. Also write your name and the problem number on
each sheet you hand in.
PROBLEM 1(30%)
The ECP plant, shown in Figure 1 is designed to
Translational Mechanical Systems
Basic (Idealized) Modeling Elements
Interconnection Relationships -Physical Laws
Derive Equation of Motion (EOM) - SDOF
Energy Transfer
Series and Parallel Connections
Derive Equation of Motion (EOM) - MDOF
Western Michiga
General Mechanical Systems
Pulley System 1
Pulley System 2
General Mechanical System Example 1
General Mechanical System Example 2
Western Michigan University-ME3600-L05-General Mechanical
Page 1
Pulley System 1
k 2x 2
k2
T
x1 T
x2
T
T
T
k 1x 1
m
k1
x=2(x
Dynamic Response of Linear Systems
Represent Responses of LTI System in Terms of
Different Causes
Free (Natural) Response
Forced Responses to Specific Inputs
Time Domain Behaviors to Represent Stable LTI
Systems Response
Transient Response
Steady-St
ME 3600
OUT: 02/12/2016
HOMEWORK SET 5
Spring 2016
DUE: 02/22/2016
Use a separate sheet to answer each problem. Write on only one side of the sheet. Write your
name and the problem number on each sheet you hand in.
PROBLEM 1 (20%)
Consider the 1st-order s
ME3600
Control Systems
Professor Rick Meyer ([email protected])
Department of Mechanical and Aerospace Engineering
College of Engineering and Applied Sciences
Western Michigan University
Course Website: https:/elearning.wmich.edu
Western Michigan Un
Standard Forms for System Models
State Space Model Representation
State Variables
Example
Input/Output Model Representation
General Form
Example
Comments on State Space and Input/Output
Model Representations
Western Michigan University-ME3600-L05a-
Example: Sliding Blocks
Find the equations of motion
Western Michigan University-ME3600-L03-Translational Mechanical
Page 1
Example: Sliding Blocks
Western Michigan University-ME3600-L03-Translational Mechanical
Page 2
Example Sliding Blocks
Western Michi
Frequency Response-Case Study
SUPPORT
POWER
WIRE
DROPPERS
Electric train derives power through a pantograph, which contacts the power
wire, which is suspended from a catenary. During high-speed runs between New
Haven, CT and New York City, the train exper
ME 3600
OUT: 01/15/2015
HOMEWORK SET 1 SOLUTIONS
Spring 2016
DUE: 01/22/2015
Use a separate sheet to answer each problem. Also write your name and the problem number
on each sheet you hand in.
PROBLEM 1 (30%)
For the systems in Figure 1,
(a) Draw a schema
Stability
Stability Concept
Describes the ability of a system to stay at its equilibrium position (for linear
systems: all state variables = 0 or y(t) = 0) in the absence of any inputs.
A linear time invariant (LTI) system is stable if and only if (iff)
ME 360 Control Systems
Partial Fraction Expansions
o Linear ordinary differential equations (ODE's) may be solved using Laplace
transforms. There are three steps in the solution process.
1. The Laplace transform is used to convert the differential equatio
ME 360 Control Systems
Examples Partial Fraction Expansions
5s + 3
( s + 1)( s + 2)( s + 3)
a) the partial fraction expansion of X ( s ) , and b) x(t ) .
1. Given: X ( s ) =
Find:
Solution: Given the characteristic equation has real, unequal roots, the pa
ME 360 Control Systems
Block Diagrams and Transfer Functions
o We can use the concept of transfer functions to develop graphical
representations of how systems function. For example, suppose that X ( s ) is
the input and Y ( s ) is the output of a system
F ( s)
f (t ), t = 0
1.
2.
3.
1
1/ s
n ! s n +1
4.
1
( s + a)
(t0 ) , unit impulse at t = t0
1, unit step
tn
e at
5.
1
( s + a) n
1
t n 1e at
( n 1)!
a
s( s + a)
1
( s + a)( s + b)
1 e at
6.
7.
1
( e at ebt )
(b a)
8.
(s + )
( s + a )( s + b)
9.
ab
s ( s
ME 360 Control Systems
Transfer Functions
Single-Input, Single-Output (SISO) Systems
o For linear systems that have a single input and a single output, we can define a single
transfer function that quantifies the dynamic behavior of the system.
o Mathemat
ME 360 Control Systems
Armature Controlled DC Motor Transfer Functions
(Reference: Dorf and Bishop, Modern Control Systems, 9th Ed., Prentice-Hall, Inc. 2001)
o In a armature-current controlled DC motor, the field
current i f is held constant, and the arm
% F-4C Aircraft Longitudinal Dynamic Analysis
%cfw_
Linear Aircraft Dynamic Motion Analysis for F-4C Aircraft
Department of Mechanical & Aerospace Engineering
Western Michigan University
%
clc
clear
close all
R2D =
180/pi;
D2R =
pi/180;
%Aircraft Data & E
ME 3600
OUT: 02/05/2016
HOMEWORK SET 4 SOLUTIONS
Spring 2016
DUE: 02/12/2016
Use a separate sheet to answer each problem. Write on only one side of the sheet. Write your
name and the problem number on each sheet you hand in.
PROBLEM 1 (20%)
Consider a sys
ME 3600
OUT: 01/29/2016
HOMEWORK SET 3 SOLUTIONS
Spring 2016
DUE: 02/05/2016
Use a separate sheet to answer each problem. Also write your name and the problem number on
each sheet you hand in.
PROBLEM 1(20%)
(a) Suppose that the system output is obtained
ME 3600
OUT: 02/12/2016
HOMEWORK SET 5 SOLUTIONS
Spring 2016
DUE: 02/22/2016
Use a separate sheet to answer each problem. Write on only one side of the sheet. Write your
name and the problem number on each sheet you hand in.
PROBLEM 1 (20%)
Consider the 1
ME 3600
OUT: 02/19/2016
HOMEWORK SET 6
Spring 2016
DUE: 02/26/2016
Use a separate sheet to answer each problem. Write on only one side of the sheet. Write your
name and the problem number on each sheet you hand in.
REMINDER: You must pass the homework to
Inverse Laplace Transform
Given an s-domain function F(s), the inverse Laplace
transform is used to obtain the corresponding time
domain function f (t)
Procedure:
Write F(s) as a rational function of s.
Use long division to write F(s) as the sum of a st
Transfer functions
Dynamic Response of Linear Time Invariant (LTI)
Systems
Free (Natural) Response
Forced Response
Transfer Function
Poles
Zeros
Free Response General Form
Input/Output Modeling With Transfer Functions
Western Michigan University-M